Abstract
The paper centers around a general class of discrete linear positive operators depending on a real parameter \(\alpha \geq 0\) and preserving both the constants and the polynomial \(x^{2}+\alpha x\). Under some given conditions, this sequence of operators forms an approximation process for certain real valued functions defined on an interval \(J\). Two cases are investigated: \(J=[0,1]\) and \(J=\)\([0,\infty )\), respectively. Quantitative estimates are proved in different normed spaces and some particular cases are presented.
Authors
Octavian Agratini
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania
Saddika Tarabie
Faculty of Sciences, Tishrin University, 1267 Latakia, Syria
Keywords
positive linear operators, Popoviciu-Bohman-Korovkin criterion, Bernstein polynomials, Szasz-Mirakjan operators, Baskakov operators, polynomial weight spaces
Paper coordinates
O. Agratini, S. Tarabie, On approximating operators preserving certain polynomials, Automation, Computers, Applied Mathematics, 17 (2008) no. 2, pp. 191-199
About this paper
Journal
Automation Computers Applied Mathematics
Publisher Name
DOI
Print ISSN
1221–437X
Online ISSN
google scholar link
[1] O. Agratini, Linear operators that preserve some test functions, International Journal of Mathematics and Mathematical Sciences, Vol. 2006, Article ID94136, pp. 11, DOI
10.1155/IJMMS.
[2] O. Agratini, On the iterates of a class of summation-type linear positive operators, Comput. Math. Appl., 55(2008), 1178-1180.
[3] F. Altomare, M. Campiti, Korovkin-type Approximation Theory and its Applications, de Gruyter Studies in Mathematics, Vol. 17, Walter de Gruyter, Berlin, 1994.
[4] D. Cardenas-Morales, P. Garrancho, F.J. Munoz-Delgado, Shape preserving approximation by Bernstein-type operators which fix polynomials, Applied Mathematics and Computation, 182(2006), 1615-1622.
[5] O. Duman, C. Orhan, An abstract version of the Korovkin approximation theorem, Publ. Math. Debrecen, 69(2006), f. 1-2, 33-46.
[6] A.D. Gadjiev, C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math., 32(2002), 129-138.
[7] H. Gonska, P. Pitul, Remarks on an article of J.P. King, Schriftenreiche des Fachbereichs Mathematik, Nr. 596(2005), Universit¨at Duisburg-Essen, pp. 8.
[8] J.P. King, Positive linear operators which preserve x², Acta Math. Hungar., 99(2003), no. 3, 203-208.
[9] B. Mond, On the degree of approximation by linear positive operators, J. Approx. Theory, 18(1976), 304-306.